My approach was to make a script that would run at shutdown. Shutdown scripts are handled at /lib/systemd/system-shutdown/, so the steps here are (1) make a script that turns the TFT backlight off, (2) put that script in the system-shutdown folder.

Make the script by doing the following:

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sudo nano /lib/systemd/system-shutdown/blanktft.sh

Paste in the following code:

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#!/bin/bash
mount -oremount,rw /
sudo sh -c 'echo "0" > /sys/class/backlight/soc\:backlight/brightness'
mount -oremount,ro /

The "mount -oremount" is for loading and unloading the filesystem. I wasn't having luck getting the script to execute without it, and I believe that's because necessary elements of the filesystem are already off when this script loads.

Save that file, then make it executable by:

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chmod +x /lib/systemd/system-shutdown/blanktft.sh

Boom. That's it!

You can test it by running the script as so:

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sudo /lib/systemd/system-shutdown/blanktft.sh

You should see the TFT turn off.

Turn it back on with:

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sudo sh -c 'echo "1" > /sys/class/backlight/soc\:backlight/brightness'

Reboot or shutdown to see it in action!